Answer:
0.47 and 11.53
Step-by-step explanation:
h = 60t − 5t²
27 = 60t − 5t²
5t² − 60t + 27 = 0
Quadratic formula:
x = [ -b ± √(b² − 4ac) ] / 2a
t = [ -(-60) ± √((-60)² − 4(5)(27)) ] / 2(5)
t = (60 ± √3060) / 10
t = 0.47 or 11.53
Answer:
2. 27
3. Option C. 3, 5, 9, 17, 33, ...
Step-by-step explanation:
2. The sequence is defined by the explicit function 
Therefore, the 5th term i.e.
of the sequence.
(Answer)
3. The explicit definition is 
Hence, 



Therefore, the option C is the right sequence. (Answer)
Answer:
x = 1
Step-by-step explanation:
Remember that the axis of symmetry is exactly halfway between the x-intercepts. Find the average of -3 and 5 to obtain this x-value: It is:
-3 + 5
x - intercept = ------------ = x = 1
2
Answer:
n = - 
Step-by-step explanation:
Given
(1 + n) = -
n
Multiply both sides by 6 ( the LCM of 3 and 2 ) to clear the fractions
4(1 + n) = - 3n ← distribute left side
4 + 4n = - 3n ( add 3n to both sides )
4 + 7n = 0 ( subtract 4 from both sides )
7n = - 4 ( divide both sides by 7 )
n = - 
Answer:
The values of x and y in the diagonals of the parallelogram are x=0 and y=5
Step-by-step explanation:
Given that ABCD is a parallelogram
And segment AC=4x+10
From the figure we have the diagonals AC=3x+y and BD=2x+y
By the property of parallelogram the diagonals are congruent
∴ we can equate the diagonals AC=BD
That is 3x+y=2x+y
3x+y-(2x+y)=2x+y-(2x+y)
3x+y-2x-y=2x+y-2x-y
x+0=0 ( by adding the like terms )
∴ x=0
Given that segment AC=4x+10
Substitute x=0 we have AC=4(0)+10
=0+10
=10
∴ AC=10
Now (3x+y)+(2x+y)=10
5x+2y=10
Substitute x=0, 5(0)+2y=10
2y=10

∴ y=5
∴ the values of x and y are x=0 and y=5